if A,B,C are angles of a triangle and none of them is equal to pi/2,then prove that tanA+tanB+tanC=tanA.tanB.tanC.
Answers
Given : A,B,C are angles of a triangle
none of them is equal to pi/2
To Find : tanA+tanB+tanC = tanA.tanB.tanC.
Solution:
A,B,C are angles of a triangle
Sum of angles of a triangle = 180°
=> A + B + C = 180°
=> A + B = 180° - C
taking tan both sides
=> tan (A + B) = tan (180° - C)
=> (tan A + tanB)/(1 - tanAtanB) = -tanC
=> Tan A + TanB = - TanC + TanATanB TanC
=> Tan A + TanB + TanC = TanATanB TanC
QED
Hence proved
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Answer:
We have to prove that tan A + tan B + tan C = tan A*tan B*tan C for any non-right angle triangle. For any triangle the sum of the angles is equal to 180 degrees. If we take a triangle ABC, A + B + C = 180 degrees.